Figured I better try a comparison of the two since I hadn't done so for
years.
ultra_wide_angle camera renders very differently so I was wrong to assume
they were more similar.

// cmd: +w300 +h300

// distortions of fisheye lens compared with ultra wide angle
camera {
// fisheye // uncomment
 ultra_wide_angle // comment
  location -z*1 // any distance
  look_at 0 // try 5 here also to see interesting effect
  up y
  right x*image_width/image_height
  angle 360 //
}

#declare Checker=
pigment {checker color rgb 0 color rgb 10 scale 0.05}

#declare Hexagon=
pigment {hexagon color red 10 color green 10 color blue 10 scale 0.05 rotate
90*x}

box {-1,1
        pigment {gradient z
                pigment_map {
                [0 Checker]
                [1 Hexagon]
        } scale 2.001 translate -z}
        scale 10
}

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